expected_coskew = [ 0.147575   0.154872   0.126323   0.154872   0.414994  -0.033756   0.126323  -0.033756   0.013083
                    0.154872   0.414994  -0.033756   0.414994   0.861588  -0.301254  -0.033756  -0.301254  -0.287069
                    0.126323  -0.033756   0.013083  -0.033756  -0.301254  -0.287069   0.013083  -0.287069   1.017824]

expected_cokurt = [ 2.126762   1.118844   0.474779   1.118844   1.122935   0.187329   0.474779   0.187329   1.155241   1.118844   1.122935   0.187329   1.122935   1.404624  -0.026636   0.187329  -0.026636   0.276558   0.474779   0.187329  1.155241   0.187329  -0.026636   0.276558   1.155241   0.276558   0.178076
                    1.118844   1.122935   0.187329   1.122935   1.404624  -0.026636   0.187329  -0.026636   0.276558   1.122935   1.404624  -0.026636   1.404624   3.102880  -0.517198  -0.026636  -0.517198   0.779222   0.187329  -0.026636  0.276558  -0.026636  -0.517198   0.779222   0.276558   0.779222   0.218735
                    0.474779   0.187329   1.155241   0.187329  -0.026636   0.276558   1.155241   0.276558   0.178076   0.187329  -0.026636   0.276558  -0.026636  -0.517198   0.779222   0.276558   0.779222   0.218735   1.155241   0.276558  0.178076   0.276558   0.779222   0.218735   0.178076   0.218735   5.989492]

# Expected skewness, kurtosis, and central moments are calculated
# using StatsBase.
# (Note: + 3 has been added to the kurtosis values, to change the
# cumulant into a standardized central moment.)
expected_skewness = [0.2036496291131231, 1.055142530854644, 0.5466699866166419]
expected_kurtosis = [3.2674593510418695, 4.065496961897709, 2.6149221488093146]

expected_third_moment = [0.14757650128987837, 0.8615880265444518, 1.0178235320342266]
expected_fourth_moment = [2.1267754676390918, 3.1028802049533724, 5.989470624146371]
